Maths-

General

Easy

Question

# What are the horizontal asymptotes for the graph

Hint:

### A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) = , where p(x) and q(x) are polynomials such that q(x) ≠ 0.

Rational functions are of the form y = f(x)y = f x , where f(x)f x is a rational expression .

- If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote.
- If the degree of the numerator is less than the denominator, then the asymptote is located at y = 0 (which is the x-axis).
- If the degree of the numerator is greater than the denominator, then there is no horizontal asymptote.

## The correct answer is: From the graph we can analyze that the vertical asymptote of the rational function is x = -3 and x = -4.

- Find the asymptotes of the rational function, if any.
- Draw the asymptotes as dotted lines.
- Find the x -intercept (s) and y -intercept of the rational function, if any.
- Find the values of y for several different values of x .
- Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.

The vertical asymptote of a rational function is x - value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

x^{2} + 7x + 12 = 0

x^{2} + 3x + 4x + 12 = 0

x(x + 3) + 4(x + 3) = 0

(x + 3) (x + 4) = 0

x = -3 or x = -4

The vertical asymptote of the rational function is x =−3 and x = -4

This function has x -intercept at (4,0) and y -intercept at (0,7) . We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x = -3 and x = -4.

### Related Questions to study

Maths-

### Tell whether the given sequence is an arithmetic sequence. 3,6,9,15,18,...

### Tell whether the given sequence is an arithmetic sequence. 3,6,9,15,18,...

Maths-General

Maths-

### Tell whether the given sequence is an arithmetic sequence. 3,6,9,12,15,18,...

### Tell whether the given sequence is an arithmetic sequence. 3,6,9,12,15,18,...

Maths-General

Maths-

### Tell whether the given sequence is an arithmetic sequence. 1,-2,3,-4,5,...

### Tell whether the given sequence is an arithmetic sequence. 1,-2,3,-4,5,...

Maths-General

Maths-

### Tell whether the given sequence is an arithmetic sequence. 77,64,51,38,25,...

### Tell whether the given sequence is an arithmetic sequence. 77,64,51,38,25,...

Maths-General

Maths-

### Tell whether the given sequence is an arithmetic sequence. 1,15,29,43,57,....

### Tell whether the given sequence is an arithmetic sequence. 1,15,29,43,57,....

Maths-General

Maths-

### Write a recursive formula for the given sequence. 47, 39, 31, 23, 15, ....

### Write a recursive formula for the given sequence. 47, 39, 31, 23, 15, ....

Maths-General

Maths-

### Write a recursive formula for the given sequence. 81,85,89,93,97,....

### Write a recursive formula for the given sequence. 81,85,89,93,97,....

Maths-General

Maths-

### Write a recursive formula for the given sequence. 81,85,89,93,97,....

### Write a recursive formula for the given sequence. 81,85,89,93,97,....

Maths-General

Maths-

### How do you find vertical and horizontal asymptotes of a rational function?

What are the vertical asymptotes for the graph of

### How do you find vertical and horizontal asymptotes of a rational function?

What are the vertical asymptotes for the graph of

Maths-General

Maths-

### Tell whether the given sequence is an arithmetic sequence. 15,13,11,9,....

### Tell whether the given sequence is an arithmetic sequence. 15,13,11,9,....

Maths-General

Maths-

### Write an explicit formula for the arithmetic sequence.

a_{n} = 12 - 5n

### Write an explicit formula for the arithmetic sequence.

a_{n} = 12 - 5n

Maths-General

Maths-

### Write an explicit formula for the arithmetic sequence.

a_{n} = 8 + 3n

### Write an explicit formula for the arithmetic sequence.

a_{n} = 8 + 3n

Maths-General

Maths-

### Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.

### Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.

Maths-General

Maths-

### Write an explicit formula for the arithmetic sequence.

### Write an explicit formula for the arithmetic sequence.

Maths-General

Maths-

### Write an explicit formula for the arithmetic sequence.

### Write an explicit formula for the arithmetic sequence.

Maths-General